Learning Rate of Regularized Regression Associated with Zonal Translation Networks

Abstract

We give a systematic investigation on the reproducing property of the zonal translation network and apply this property to kernel regularized regression. We propose the concept of the Marcinkiewicz–Zygmund setting (MZS) for the scattered nodes collected from the unit sphere. We show that under the MZ condition, the corresponding convolutional zonal translation network is a reproducing kernel Hilbert space. Based on these facts, we propose a kind of kernel regularized regression learning framework and provide the upper bound estimate for the learning rate. We also give proof for the density of the zonal translation network with spherical Fourier-Laplace series.

Keywords

• kernel regularized regression
• learning theory
• convolution translation network
• reproducing kernel Hilbert space
• Marcinkiewicz–Zygmund inequality
• quadrature rule